A trajectory of the moving point on the screen, such as a pen stroke in electronic ink or a trace of a vector-EKG, is defined typically by a multi-component signal representing the trajectory in parametric form. For example, a pen stroke in simple electronic ink is a plain curve defined by a two-component parametric representation, i.e. a sequence of sample points specified as coordinate pairs. Space curves defined by a three-component parametric representation can be provided, in particular, by advanced graphic tablets sensitive to the distance between pen and the surface of the tablet. A number of extra components, representing physical entities other than spatial coordinates, may be provided in addition to parametric representation of a curve. For example, variable-thickness lines drawn by means of pressure-sensitive graphic tablets are plain curves defined by a three-component sequence of samples, in which an extra sample, representing pressure, is added to each pair of coordinate samples.
Graphical representation of signals often suffers from noise. For example, visual quality of electronic ink may be affected by combined noise of motor tremor and digitization, especially in hand-held devices. There are many filtering techniques for denoising of graphically represented signals. One common approach is to apply a low-pass digital filter to every component, or a subset of components, in the sequence of samples as they are coming from the trace generator. This approach allows for on-the-run denoising (smoothing) of the pen stroke since the filtering delays, in terms of time and arclength, may be short enough to keep the processing unnoticeable to a user.
However, low-pass filtering typically distorts the shape of resulting curves. For example, in cursive writing, relatively small fragments may be very important for visual perception with respect to both legibility and aesthetic appearance, but noise in electronic ink often creates disturbances that are comparable in size with these critical fragments. Generally, the coordinate signals of handwriting and drawing, and the noise in electronic ink tend to have partially overlapped spectra. When filtering electronic ink, such overlapping tends to cause shape distortion and residual noise. Additional complications may also arise due to high variability in the individual manner of handwriting and in hardware-specific noise. Typically, as a result of low-pass filtering, the sharp cusps in electronic ink are cut, the critical fragments of handwriting are partially lost to smoothing, and handwritten lines look like they are somewhat shrunk in a vertical direction.
A number of existing techniques allow smoothing without the appearance of shrinking. A technique involving adaptive parameterization to address both the local distortion and overall shrinkage effects of low-pass filtering is disclosed in U.S. patent application Ser. No. 11/013,869 invented by B. E. Gorbatov et al. and entitled System and Method for Handling Electronic Ink (hereinafter “Gorbatov”), the teachings of which are hereby incorporated by reference. Gorbatov uses a low-pass smoothing filter to run a repetitive trial-and-error procedure of discarding excessive sample points and displacing the remaining sample points. A low-pass approximation filter is applied to generate a trial version of a curve each time a sample point under testing is removed from the current parametric representation and remaining sample points are displaced to correct shrinkage. The rarified and displaced sample points are filtered each time as parametrically equidistant points, resulting finally in parametric representation adapted to some extent to the chosen filter.
Filtering with adaptive parameterization, as described above, provides better denoising, better visual quality of electronic ink, and reduces data size. However, the method requires a whole pen stroke or significant part of it to be involved in iterative processing and, therefore, makes it impossible to hide the processing from the user.
The above described method reflects the state of advanced, in terms of the noise and shrinkage reduction, techniques to expand the processing over an enlarged part of a trace behind the moving point, thus keeping that part in transitional state. Such techniques, when applied to electronic ink, are often used to refresh the whole pen stroke after it is finished, after a pen-up event.